I am sure that this has been reported before.
In each case the solution is 1/3ln(t~-3)-1/3ln(t~+3). Maple does not recognize the domain of the integrand at all and we have the log of a negative number. Ugly.
If you allow for the constant of integration to be complex, then the result makes sense. If you evaluate this anitiderivative between real limits, you will get a real answer.
I do realize, however, that this is diﬃcult to explain to a beginning calculus student when you’re trying to teach them Maple.
From the online help of ‘int’ the statement:
Note that no constant of integration appears in the result.
Therefore the integral of an real valued integrand can have a constant imaginary part;
For -3 < t < 3 this is a real valued expression.
and Maple will recognize the assumption made on t.